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Continuity And Differentiability

Question

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$Find space dy over dx space where space left parenthesis straight x squared minus straight y squared right parenthesis squared equals 4 xy$

Solution

Here space left parenthesis straight x squared minus straight y squared right parenthesis squared equals 4 xy Differentiating space both space sides space straight w. straight r. straight t space straight x comma space we space get comma space space 2 left parenthesis straight x squared minus straight y squared right parenthesis open parentheses 2 straight x minus 2 straight y dy over dx close parentheses equals 4 straight x dy over dx plus 4 straight y.1 therefore space 4 straight x left parenthesis straight x squared minus straight y squared right parenthesis minus 4 straight y left parenthesis straight x squared minus straight y squared right parenthesis dy over dx equals 4 straight x dy over dx plus 4 straight y therefore space left square bracket straight x plus straight y left parenthesis straight x squared minus straight y squared right parenthesis right square bracket dy over dx equals straight x left parenthesis straight x squared minus straight y squared right parenthesis minus straight y therefore space dy over dx equals fraction numerator straight x left parenthesis straight x squared minus straight y squared right parenthesis minus straight y over denominator straight x plus straight y left parenthesis straight x squared minus straight y squared right parenthesis end fraction

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